Problem: Five couples were at a party. If each person shook hands exactly once with everyone else except his/her spouse, how many handshakes were exchanged? (Note: One obviously doesn't shake hands with oneself.)
Solution: There are a total of 10 people at the party.  Each shakes hands with everyone else, except for their spouse, which will be a total of $10-2=8$ other people.  The total number of handshakes will be $10\cdot8/2=\boxed{40}$, where we divide by 2 to correct for counting each handshake twice.